Boundary Stabilization of a Degenerate Euler-Bernoulli Beam under Axial Force and Time Delay
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912779389108224 |
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| author | Siriki, Ben Bakary Junior Coulibaly, Adama |
| author_facet | Siriki, Ben Bakary Junior Coulibaly, Adama |
| contents | This paper provides a qualitative analysis of a non-uniform Euler-Bernoulli beam with degenerate flexural rigidity, subjected to axial force and boundary control with time delay $τ> 0$. By reformulating the system as an abstract evolution problem in an augmented Hilbert space incorporating weighted Sobolev spaces, we employ semigroup theory to ensure well-posedness. Using the energy multiplier method and a non-standard Lyapunov functional featuring weighted integral terms, we establish uniform exponential energy decay and provide a precise decay rate estimate. This work extends the results of Salhi et al. \cite{salhi2025} and Siriki et al. \cite{siriki2025} by incorporating axial force and generalized control laws, including rotational velocity control. The proposed framework offers a robust approach for analyzing complex distributed systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Stabilization of a Degenerate Euler-Bernoulli Beam under Axial Force and Time Delay Siriki, Ben Bakary Junior Coulibaly, Adama Analysis of PDEs This paper provides a qualitative analysis of a non-uniform Euler-Bernoulli beam with degenerate flexural rigidity, subjected to axial force and boundary control with time delay $τ> 0$. By reformulating the system as an abstract evolution problem in an augmented Hilbert space incorporating weighted Sobolev spaces, we employ semigroup theory to ensure well-posedness. Using the energy multiplier method and a non-standard Lyapunov functional featuring weighted integral terms, we establish uniform exponential energy decay and provide a precise decay rate estimate. This work extends the results of Salhi et al. \cite{salhi2025} and Siriki et al. \cite{siriki2025} by incorporating axial force and generalized control laws, including rotational velocity control. The proposed framework offers a robust approach for analyzing complex distributed systems. |
| title | Boundary Stabilization of a Degenerate Euler-Bernoulli Beam under Axial Force and Time Delay |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.18179 |